I'm talking about repurposing an existing house, often with very minor or no modifications. But as you can read about if you look for "single-family zoning"[1] this is often illegal.
Of course you can also destroy existing houses and re-build, or build new houses, but then you're back to the GP's point that that will often take time. Repurposing existing buildings can often be done very quickly.
You'll also get "new housing" that you'd never get without it, even if you had sufficient money. E.g. my example of an older couple that might keep their house for life, and would never consider moving, but they might consider accepting a tenant in their (mostly unused) basement or large garage.
Interestingly e.g. California seems to have made this legal in 2021[2], but I'm not sure about the specifics there. In jurisdictions I know about it's often de-facto illegal, because other building code often mandates such extensive modifications as to make it impossible. E.g. insisting that each address has its own dedicated entrance into the building.
E.g. where I'm from (Iceland) some older houses are set up as duplexes where there's a single entrance, and a small area shared by both houses, usually to hang your coats, store your shoes and other outwear, and very usefully a shared laundry room (a single family's laundry facilities are rarely used all the time). Such setups have since been made illegal for new housing by zoning regulations.
There's been similar moves towards "one size fits all" zoning in most or all other western countries. E.g. in New York it used to be common for younger people or new immigrant families to live in housing where several families might share kitchen facilities or other common areas. I.e. essentially being set up as collage dorms. That's since been made illegal for any "real" housing, which has resulted in driving up the price of housing, and pricing some people out of the market entirely.
1. https://en.wikipedia.org/wiki/Single-family_zoning
2. https://www.californiacitynews.org/2021/09/california-says-g...